In the logical approach to information retrieval, retrieval is considered as uncertain inference. Here we present a new, powerful inference method for this purpose which combines Datalog with probability theory on the basis of intensional semantics. We describe syntax and semantics of probabilistic Datalog and also present an evaluation method and a prototype implementation. This approach allows for easy formulation of specific retrieval models for arbitrary applications, and classical probabilistic IR models can be implemented by specifying the appropriate rules. In comparison to other approaches, the possibility of recursive rules allows for more powerful inferences. Finally, probabilistic Datalog can be used as a query language for integrated information retrieval and database systems.